by William A. Edelstein, Ph.D.
Member, Board of Directors
New Yorkers for Verified Votingw.edelstein@gmail.com
November 14, 2006

Summary

As New York decides on new voting systems, one key
question is this — how many voters can be served by each voting
machine? This number is critical in order to estimate costs as well
as to avoid long lines for voters. The New York City Board of Elections
recently released a report saying that New York should replace each
lever machine by 1 full-face-ballot computer DRE voting machine with
voter verified paper trail. Assuming that each voter will take 3.25
minutes to vote, they calculate that 277 voters can vote on each DRE
in a 15-hour election Day. However, the report neglects the effect
of non-uniform voter arrivals, DRE outages and extra time needed by
voters using special accessibility aids on DREs. We have applied queuing
theory, the mathematical study of waiting lines, to carry out computer
simulations of realistic elections. We use a scenario with more voters
arriving at peak times—early
morning, lunch and early evening hours—as is typical during elections.
According to our calculations, a ratio of 277 voters per DRE would
cause unacceptable wait times of 1-hour or longer. Recent elections
with DREs have produced extremely long lines in many places around
the country, causing would-be voters to leave, thereby disenfranchising
them. In order to guarantee reasonably short wait times—even
without taking into account DRE outages and the use of DRE special
voting aids—our
results indicate that each DRE in New York should be allocated to no
more than 150 voters, which means replacing each lever machine by 3
DREs. But the acquisition and maintenance cost of this many electronic
voting machines would be excessive. In contrast, precinct based, paper
ballot optical scan systems use simple, inexpensive marking booths
that are the equivalent choke points to DREs. These paper ballot scan
systems can be easily and economically configured to eliminate lines.

Early in 2007, New York counties will choose either direct recording
electronic voting machines (DREs) or paper ballot-scanner systems (PBOS)
to replace lever voting machines. How many new voting machines will
be needed? The answer to this question is critical for ensuring that
each county's voting will go smoothly and that costs will be within
reason.

Long lines have occurred during elections with DRE use in California,
Florida, Maryland, Mississippi, Ohio, Pennsylvania, Tennessee, Utah
and other states1-9 and
have caused some voters to give up and go home, effectively disenfranchising
them. It is prohibitive to buy a large number of DREs because of their
cost, which makes it likely that a substantial number of voters using
DREs will end up in long lines. In contrast, PBOS uses inexpensive
marking booths whose numbers can be increased to eliminate lines and
long waits.

Long voter waits—and consequent disenfranchisement of those who cannot
wait—may prove to be a fundamental and disqualifying problem for DREs.

The New York City Board of Elections recently published a report entitled
"An Analysis of the Number of Voters per Voting Machine"10 which
omits several important considerations and contains a number of doubtful
assumptions. The result is a serious underestimate of the number of
DREs that would be needed to serve the voters of New York City as well
as a misunderstanding of relevant aspects of paper ballot-scanner systems.

The New York City Board of Elections report:

Incorrectly assumes that a maximum of 50% of voters will appear
at any election;

Does not take into account the extra time needed to vote on
DREs by persons with disabilities;

Does not take into consideration the uneven arrival of voters,
particularly during peak voting hours, and potential voter traffic
jams;

Does not include the effects of machine and procedural breakdowns.

Properly taking these factors into account substantially decreases
the number of voters that could use a voting machine in a day and considerably
increases the number of DREs that would have to be purchased and maintained.

In their examination of the use of DREs in the recent Cuyahoga, Ohio
primary, the Election Science Institute carried out a queuing theory
analysis of the potential for long lines.11 Following their approach,
we have done our own queuing theory simulation of voting statistics.
If we accept the New York City Board of Election report’s figure
of 3.25 minutes to vote on a DRE with voter verifiable paper trail—which
the report claims will allow 277 voters to use a single machine in
a 15 hour voting day—then our study shows that a significant
fraction of such elections will have maximum voter waits of over an
hour to cast their ballot. This will happen even without the all too
common experience of DRE breakdown; it also will occur even if we do
not factor in extra time for voters with disabilities. Details of our
calculations are given in the full report.

The only way to guarantee short lines is to have a large overcapacity,
i.e., to have many more voting systems than would be needed for the
average voter flow. This is not practical with DREs because of their
high cost. However, New York counties could avoid long lines and save
money by choosing paper ballot scanner systems. In the 2004 general
election, Lee, Massachusetts accommodated 3200 voters on a single paper
ballot scanner12 and Londonderry, New Hampshire13 processed more than
12,000 voters on two scanners in a 13 hour Election Day. Voters mark
their ballots in inexpensive marking booths, and there were no lines
waiting to mark ballots or to use the scanners in these towns. The
number of marking booths can be increased at low cost to avoid any
problems of voter traffic congestion and long lines.

Factors not fully considered by the New York City report

Voter turnout will be significantly higher than 50% at some pollsites

The New York City report10 assumes that a maximum of 50%
of registered voters will appear in any election and calculates the
number of machines they will order based on this assumption. While
the average turnout for New York’s 5 counties (New York, Bronx,
Kings, Queens and Richmond) was indeed 50% in the 2004 general election,
many areas had higher figures.14,15 So to guarantee efficient
access to the polls, it is necessary to consider the peak vote, which
could occur in any election precinct.

Figure 1. Number of New York City
Assembly Districts vs. % turnout in the 2004 general election.
Each bar represents how many Assembly Districts had turnout
in the range covered by the bar. There were 6 districts that
had turnout between 40%-42%, 5 districts had turnout between
42%-44%, 1 district between 44%-46%, etc.

Figure 1 shows the number of Assembly Districts
in New York City Counties vs. their votes for President in the 2004
election.14,15 There are many Assembly Districts where the turnout
was well above 50%, indeed approaching 60%. Since these are averages
over Assembly Districts, it is apparent that some election precincts
within these Districts must have had higher turnouts than 60%. Statewide,
over 60% of voters showed up. (The Lee, MA and Londonderry, NH examples
cited above had over 80% turnout in 2004.)

The 2004 NY data suggests that an estimate of 75% as an upper bound
for voter turnout would be appropriate. This is the same percentage
that has been used by New York City to determine how many lever voting machines
should be deployed. An underestimate of the number of machines could
lead, at least, to serious voter traffic flow problems, long waits
and extended Election Days. At worst, it can lead to voter disenfranchisement.

This occurred in the 2004 general election in Florida and Mississippi.1,2
In Ohio long lines caused voters to give up and leave without voting.4
There were more long lines in the recent 2006 primary in Cuyahoga County,
Ohio.11 There were long lines—along with other DRE issues—in the
September 2006 problematic primary in Maryland.3 Insufficient
DREs and DRE malfunctions caused more long lines and voter frustration
in a number of places in this year’s general election on November 7
(e.g. refs. 5-9).

People with special needs will take much longer than 3.25 minutes
to vote on DREs

The New York State Board of Elections studied the time needed for
persons with special needs to vote with ballot marking devices.16 This
varied from 18 to 45 minutes among the several systems and types of
accessibility aids considered. Voting on DREs using accessibility aids
would be similar.

The New York State Board of Elections (NYBOE) has hired the American
Institutes for Research (AIR)17 to test voting machines and answers
are supposed to be coming in the next few months. Part of their charge
is to estimate how many voters would use accessibility aids. This would
include, for example, voters with visual, dexterity, or mobility impairments
who would use the audio interface or sip and puff controls. It might
also include voters who are not comfortable with computers, touchscreens,
or the use of English.

A small number of voters with special needs, each taking 30 minutes
to vote, would have a profound effect on numbers of voters able to
use a DRE on Election Day.

Voters do not arrive at exact intervals

The New York City report allots an average of 3.25 minutes for each voter to
use a DRE with voter verifiable paper record. 900 minutes (a 15 hour
Election Day) divided by 3.25 is 277. They then assert that a single
DRE can accommodate 277 voters, and propose to buy one DRE for each
554 registered voters on the basis of a 50% turnout. However, the New York City
report does not properly take into account the effect of fluctuations
of voter arrival. It says:

On Election Day, there are "peaks and valleys"
of usage by voters depending upon the time of day, the weather, traffic
and other variables outside of the control of election staff. Thus
there will always be times when voters are waiting, but on the whole,
there should be some insurance that waits will not be over long durations
throughout the day and that on the whole, voting can be accomplished
expeditiously. If we make the assumption that on the whole elections
are conducted expeditiously by the survey jurisdictions, than [sic]
a maximum that is at, or somewhat higher than, the average by type
of technology should be a reasonable maximum for New York.10

These unsupported assumptions are contradicted by DRE delays around
the country1-9 and the mathematics of queuing theory that governs the
voting process.

We begin our election simulation by assuming 277 voters per DRE estimated
by the New York City report. We take a scenario with heavy voter arrivals from
6am to 8am, 12pm to 1pm and 5pm to 7pm, where voters arrive at double
the rate of the rest of the day, and no DREs break down. If the whole-day
average is 18.5 arrivals per hour, then the slow periods will have
14 per hour and the fast periods 28 per hour.

There will be many voting locations where only a small number of DREs
will be needed,10 so we have focused—as examples—on pollsites with
1, 2 or 4 DREs. Sites with more DREs will behave proportionally.

With these conditions, over 80% of precincts with 1, 2 or 4 DREs will
have voters waiting for more than an hour. Voters will have a maximum
wait of more than 1-1/2 hours in 38%, 17% and 3% of precincts where
there are 1, 2 or 4 DREs, respectively.

If we have 150 voters per DRE—approximately the ratio of privacy booths
to voters specified by statute in NH, scaled by the different Election
Day lengths in NH (13 hours) and NY (15 hours)—then there will be few
voters waiting more than thirty minutes.

DRE outages will cause further delays. The present reliability guidelines
allow over 9% of voting machines to fail in a 15-hour day,18 and ESI
uses a one-hour average repair/replacement time in some of their calculations.11

The bottom line is that even with many more DREs than recommended
by the New York City report,10 queuing statistics guarantee that a substantial
number of voting precincts will have voters with very long waits. In
order to avoid long lines at DREs for all precincts, it is necessary
to have a large excess capacity of voting machines. With DREs, this
is not realistic because of their high acquisition and operating costs.

The following examples of voting by paper ballots and ballot scanners
show how PBOS systems can eliminate long voter queues at a minimal cost.

Lee, Massachusetts uses PBOS. They had 4,000 registered voters and 3,200
(80%) used 35 privacy booths and one scanner in the 2004 election. The
Lee town clerk says that they had no lines at the privacy booths in the
2004 election, whereas they had "long, long lines" when they
had previously used 8 lever machines.12

Londonderry, New Hampshire has 15,029 registered voters and 12,229 (81%)
of them voted in the 2004 election.13 They
use PBOS and have two scanners. Each scanner therefore processed about
6114 ballots which is equivalent to 7055 ballots in a 15-hour day. (Note--even
if we changed this by a factor of two to accommodate undervote notification
in NY, each scanner could still handle 3527 ballots in a day.)

Londonderry has 100 privacy booths, each of which served an average
of 122 people in their 13 hour Election Day in 2004, equivalent to 141
voters per NY’s 15 hour Election Day. The town clerk said that there
were no lines at the privacy booths. New Hampshire requires a privacy
booth for every 125 voters. Just in case more voters show up, she has
extra cardboard privacy screens that can be placed on tables.

During a heavy election, the Londonderry town clerk estimates that only
10% of booths will be filled much of the day but 90% are occupied during
peak times.

Since the scanners only count ballots but do not record the votes, a
stopped scanner does not halt the election, unlike DRE failures. If the
scanner is down, the ballots are placed in a special compartment in the
ballot bin and scanned later. The Londonderry town clerk has supervised
25-50 elections over the last 7 years and has experienced only one scanner
breakdown. A replacement scanner was brought over and put into service
in less than an hour.

These examples show the kind of overcapacity that works. It is easy
to achieve with PBOS since the privacy booths cost about $150 each. In
reality, it would take more than 100 DREs in Londonderry, New Hampshire
or 35 DREs in Lee, Massachusetts to achieve the same ease of use since
1) DREs have a much greater breakdown rate than scanners and 2) voters
with disabilities would take up a lot of DRE capacity. In contrast, ballot
marking machines that go with PBOS are separate devices that do not affect
flow of voters in other privacy booths or the operation of the scanners.

How many voting machines do we need?

Direct Recording Electronic Voting Machines (DREs)

The New York City report suggests that each DRE could serve 277 voters
on Election Day. Assuming a 50% turnout, they conclude that one DRE should
be purchased for each 554 voters, which is not too different from what
the report says is an average of 1 lever machine for 600 voters. In other
words, they recommend replacing each lever machine by a single DRE.10

Our study shows that 277 voters per machine is unrealistic (given the
New York City voting time figure of 3.25 minutes) and will lead to very long waiting
times in some election districts. We believe a realistic ratio that keeps
lines down everywhere would be more like 150 voters per DRE. Trying to
serve even this number of voters with one DRE may prove problematic because
of DRE outages and long voting times for persons with special needs.
Taking 150 voters per DRE and a possible 75% turnout implies a DRE for
each 200 registered voters. The replacement ratio then becomes 3 DREs
for each lever machine.

The time for each person to vote (3.25 minutes) in our calculation was
taken from the New York City report and could change when the "usability study"
is completed by AIR. Any figures then obtained can—and should—be used
for a queuing analysis similar to what we have done here.

Paper Ballot, Ballot Marker, Optical Scan Systems (PBOS)

The examples above from Londonderry, New Hampshire and Lee, Massachusetts
demonstrate that a large overcapacity, i.e. one privacy booth for 125
voters (Londonderry, New Hampshire ) or per 90 voters (Lee, Massachusetts)
essentially eliminated the experience of voting bottlenecks. This is
a simple and inexpensive solution which would improve the voting experience
in New York, as it did when Lee, MA went from 8 lever machines for 3200
people to 35 privacy booths.

If we scale the New Hampshire number from a 13 hour day to a 15 hour
day, then one needs approximately one privacy booth for each 150 voters
who show up. Assuming a 75% turnout, we therefore need a privacy booth
for each 200 registered voters. As is done by the Londonderry, New Hampshire
town clerk, it is a good idea to have a number of additional folding
cardboard privacy screens that can be placed on tables in case more voters
come.

As mentioned above, ballot marking devices that would be used by voters
with disabilities will not affect the voting process for other voters.
With this option, election commissioners have to determine how many disabled
voters will vote in their election district and buy enough ballot marking
devices to serve their disabled constituents. Commissioners should be
aware that as voters with disabilities become more familiar with new
voting technology, their attendance at polling sites will increase.

Acquisition Costs

A simple calculation for a pollsite with 2,000 registered voters shows
how PBOS could save $45,500 in acquisition costs compared to buying DREs.

According to our figures above, this pollsite would require 10 DREs
at approximately $8,000 each or $80,000.

The same pollsite could be served by a single optical scanner ($5,500)
and 10 marking booths ($150 each, $1,500). It would also need ballot
marking devices for the disabled.

We now calculate the number of ballot marking devices needed. Let us
assume a 75% turnout (1,500 voters), that 5% of those voters (75) need
special access and that each takes 30 minutes. 900 minutes divided by
30 minutes is 30. There will be a similar queuing problem for the ballot
markers as there was for the DREs, so that number should probably be
decreased by a factor of 2 to 15. Then the district should buy 5 ballot
marking devices at about $5,500 each which comes to a total of $27,500.

Thus the total is $5,500 + $1,500 + $27,500 = $34,500 for PBOS and ballot
marking device acquisition costs, $45,500 less than the figure for DREs.

Conclusions: DREs will cause long lines; PBOS can eliminate lines

The use of DREs has created long lines in many constituencies around
the country. The nature of voter arrival statistics is such that there
may be a large variability in the waiting times for different voting
locations as governed by the mathematics of queuing theory. The only
way to avoid long waiting times for voters is to have a large overcapacity,
i.e. many DREs or many marking booths for use with PBOS. This is only
economically possible with PBOS, as DREs ($8,000) represent the equivalent
choke point in the voting process as the marking booth ($150).

DRE outages (10% in recent experience) and long voting times for persons
with special needs represent further potential serious slowdowns on Election
Day.

We believe that 30 minutes should be the maximum waiting time for voters.
Many of them may be taking time off work, have to manage accompanying
children or have medical conditions that make it difficult for them to
stay at the polling place for extended times. Every precinct that follows
the advice of the New York City Report to allocate one DRE for each 277
actual voters will exceed that standard. Most will have maximum wait
times of at least one hour, and a significant number will have wait times
greater than 1-1/2 hours.

Recent experience shows that such a result produces frustration or hardship
for voters and many will leave rather than wait in long times. The analysis
in the full report shows that numerous polling places allocating 1 DRE
for each 277 voters will also have substantial overtimes, creating long
workdays for election workers. 150 voters per DRE might work reasonably
well, although the picture is clouded by DRE breakdown and use by disabled
voters.

These numbers are similar to those in a story about a voting precinct
with 2 DREs in Nashville, Tennessee. Elections went well with 214 voters
(107 per DRE) but had long lines with 527 voters (263 per DRE).5

Some Cleveland Election Commissioners want to scrap their DREs and change to PBOS. As one election official put it, "Electronic voting systems are not scalable to meet demand on Election Day." Unlike optical scan or punch cards, where you can simply add inexpensive voting stations, there are not additional DRE (touch screen) machines available."19

The correct and smooth functioning of elections is fundamental to democracy.
Everything compatible with election integrity should be done to make
the process voter-friendly—overlong waits are unacceptable. If a city
has hundreds of precincts and ten of them have multi-hour waiting lines
or Election Day delays which force voters to continue well beyond midnight—as
happened in Ohio in 2004—voters will blame election commissioners and
other government officials for not having enough machines. People will
leave without voting; this amounts to disenfranchisement of those voters.
There will be angry charges that the election has been compromised or
manipulated.

The uneven flow of voters on Election Day means that the only way to
guarantee equal voter access in terms of the time it take to vote is
to have a sizable overcapacity in every district. Both acquisition and
operating costs make that economically prohibitive with DREs. More machines
mean higher operating costs as well as higher acquisition costs. To provide
for reasonable waiting times, it will be necessary to have three times
as many DREs as the New York City Board of Election suggests. In contrast,
it is eminently feasible to have negligible lines for PBOS systems, because
it is possible to supply a large number of inexpensive privacy booths
for marking ballots.